If you file for divorce, you can ask for possession of the marital residence. You can ask for spousal support as well... but the issue here is that your marriage was only 4 years, and because of that, alimony is not likely to be awarded for a very long period of time (if at all).
There is a very good chance that you could get temporary possession of the residence and he would be ordered to pay during the divorce proceedings. But there is very little chance that a court would order him to pay for your house after the divorce for a long period of time.
Generally, the way a court divides marital property is that everything is divided roughly equally. That is, everything that was accumulate during your 4 years together would be split 50/50 (generally). But if there is an asset, in this case the house, and there was equity in the home... that equity would usually be divided. So if you kept the house, you would have to offset that value elsewhere (give him money or property to even it up more). Then going forward, the burden of the mortgage would be to whoever kept the house. Alternatively, the house can be sold and the profits divided.
If the earnings are very unequal it is possible that he might have to pay alimony for a while. But after 4 years of marriage, there is almost no chance that he would be ordered to pay for your house forever.
Sorry, I know this is not what you hoped to hear, but this is the reality of your situation. My policy is to just deliver the truth, keep in mind that I did not make the law here... I am just relaying accurate information to you.