I dated a Hispanic man for a good long time. You are right, his family was very close and it was a beautiful thing. But, there were no mulit generations living together.
I would NEVER agree to what your in-laws are proposing. When a man marries, he leaves his mommy. You say she is strict and I guarantee you, she will be motherly and you two will never will be treated like the married adults you are. You will have no say in how the kitchen and other rooms of the house are decorated and you will be using ALL of their furnishings elsewhere in the house.
You two need to eek out your own lives, not spend your money paying for your in-laws mortgage. What happens if you get pregnant in the next five years? Then it will be even harder for you to have the money to leave. I would never want to be under the same roof with my in-laws for so many reasons. This is supposed to be some of the best years of your married lives and he is going to be living with his mommy? You should be saving for YOUR future, not paying your in-law's mortgage on a long term basis.
MAYBE live there until you graduate from college, but THAT's IT. Otherwise, I guarantee it, you will regret it.