You are married, so that marital status must be accurately recorded on the application. If he is not living in the household, that has to be explained. It is so ridiculously easy to check up on you & your husband that if you lie, you're going to prison on felony fraud charges, no doubt about it.
There's a long waiting list for Sec 8. Priority goes to the elderly and totally disabled, i.e. those who are totally incapable of working any longer. Then comes those who are either elderly or disabled. You are obviously are young and able to work. It takes typically 4-6 years now to get Sec 8 housing after an application is approved unless you are elderly & disabled. Some people are on the lists so long that by the time their name comes up, they no longer qualify.
Get to work and rent an apartment.