Aside from different diseases and the possibility of the mice being eaten, The obvious problem is going to be size. If you've seen the difference in size in breeding males and females between the two animals, you'll realize there's QUITE a problem. A breedable rat to a breedable mouse would be just silly. It'd be like breeding a teacup chihuahua to an adult great dane. Put an average litter of new born rat pups next to a female mouse, and ask yourself, "could that possibly be supported?" And then of course on the other side of things,I would assume that the male mouse would be terrified of the female rat, not think, "hey pretty lady, how you doing?"