I can imagine some of your conservative churches doing that. However, I think they should be willing to consider people of the same religion in different denomination.
As for your husband, I hope that he doesn't agree to their stipulation. However, if you and him is desperate I can see you doing it. Sometimes being able to take a stand requires that the person be relatively able to afford the necessities of life. I hope you and him will talk it out and decide what to do.
I am sending a prayer for God's wisdom and guidance your way.