House training a 3 month old Saint Bernard pup

Question
My husband and I just got a Saint Bernard puppy about a week ago and have been working on house training him. We take him out after meals, after naps and very often all day and night, but regardless of how many times we take him out, he still pees just a few minutes after coming back inside even though he seems to empty his bladder outside. When he naps, he just pees all over himself. He doesn't wake up to pee, he just sleeps right through it. He doesn't understand to follow when we call him yet, so we have to carry him outside when we want him to go. We praise him excessively when he's finished and reward him with treats, but he doesn't seem to respond well to the positive attention. I'm 19 weeks pregnant and can't carry him to and from the backyard for much longer since he has already gained so much in weight and size since we got him. He seems to never stop peeing. He goes plenty outside, doesn't drink very much water all day (he's still cautious of our kitten and doesn't like to be where the kitten is so he stays away from the kitchen most of the day) and we are always taking him out. We stop him when we catch him going in the house, tell him "No!" and take him outside, and praise him after he goes... but regardless of that he still goes barely five minutes after coming back in, and pees on himself several times during naps. We don't know what to do, and I have never had a dog that was comfortable to sleep in his own urine.

Answer
For what you are doing, you should be getting better results.  Have you talked to the vet about it?  Wetting himself in his sleep isn't normal and may have a physical problem.  

When you have him outside, make sure he walks around to stimulate urination.  

I am almost afraid at his age, he has had poor care and formed bad habits that will take time to correct.  

You may find some of this material helpful.
Much of housebreaking is not training the puppy, but making it easier for your puppy, you, and your carpet while its body to catches up to its instincts. At around 8 weeks when the puppy goes to its new home, the time from when it realizes it has to go, and when it can't wait any longer is a matter of seconds. Only time will fix that. You can hardly be expected to be attentive enough to avoid all accidents. There is no sense punishing the puppy for your inattention. It is not fair to punish you either, but you still have to clean it up if you didn't have the puppy outside in time.

Housebreaking starts before you get home with the new puppy. If you don't have a crate, buy one. I prefer the more enclosed, den like plastic ones. Skip the bedding. At first it gets wet, and later it can be chewed into choking hazards. A wire grid in the bottom will help keep the puppy up out of accidents at first. They are available with the crates, but expensive and hard to find. A piece of closely spaced wire closet shelving from a home supply place is cheaper. I am now using a plastic vegetable bin with plenty of holes drilled in the bottom. It helps block off part of the crate for the smaller puppy. If you already have a metal crate, covering it may help. Just make sure you use something the puppy can't pull in and chew. Dogs that start out in crates as little puppies, accept them very well. Never leave an unattended puppy loose in the house. If nobody can watch it, put it in the crate. I suggest letting the dog have its crate all its life. A crate needs to be just big enough for a dog to stretch out in.

Choose a command and spot you want it to use. The less accessible to strays, the less chance of serious disease. If it is a female, choosing a non grassy spot will avoid brown spots later. When you bring it home, take it to the spot and give it the command in a firm, but friendly voice. Keep repeating the command and let the puppy sniff around. Sometimes you need to walk it around to stimulate its body to eliminate.  If it does anything, praise it. Really let it know what a good dog it is and how much you love it, and maybe a treat. Note, being out there not only means you can praise it, but it also keeps it from being snatched by a hawk. If it doesn't go, take it inside and give it a drink and any meals scheduled. A young puppy will need to go out immediately afterward. Go to the spot and follow the above routine. Praising it if it goes is extremely important. If it doesn't go, take it back inside and put it in its crate and try again soon. Do not let it loose in the house until it does go.

At first it is your responsibility to know and take the puppy out when it needs to go. It needs to go out the first thing in the morning, after eating, drinking, and sleeping. If it quits playing, and starts running around sniffing, it is looking for a place to go. Take it out quickly. You will just have to be what I call puppy broke until it is a little older. How successful you are depends on how attentive you are.

By the time most dogs are about 3 months old, they have figured out that if they go to the door and stand, you will let them out. The praise slowly shifts to going to the door. Some people hang a bell there for the dog to paw. If your dog doesn't figure this out, try praising it and putting it out if it even gets near the door. When you catch it in the act, give it a sharp ''Ah, ah, ah!'' and take it out. Clean up accidents promptly. I mostly keep the little puppies out of the carpeted rooms. Still I need the can of carpet foam sometimes. First blot up all the urine you can with a dry towel. Keep moving it and stepping on it until a fresh area stays dry. A couple big putty knives work well on bowel movements. Just slide one under it while holding it with the other. This gets it up with a minimum of pushing it down into the carpet. This works with even relatively soft ones, vomit, dirt from over turned house plants, or anything else from solids to thick liquids. Finish up with a good shot of carpet foam. Note, do not let the puppy lick up the carpet foam. Once the dog is reliably housebroken, your carpet may need a good steam cleaning.

Many people strongly strongly push cleaning up all evidence of past accidents. I am slower to suggest that. Dogs will return to the same spot if they can find it. When you see one sniffing the spot, that is your clue to run it out.