I have know many, many folks over the decades where spouses started as participants in two churches. There are many different kinds of improvements to the situation.
One approach is to respect each other's beliefs. It is the Church's teaching that other Christians are indeed Christians and have a portion of the deposit of faith. You might consider occasionally attending church at a church acceptable to your husband. It could be his church or another. Continue to attend Catholic church on your own, when you can. Let him know that he is welcome to attend, as any non-Catholic always is.
Some folks here might not consider it a step forward for the two of you to be praying together in a non-Catholic church. I would disagree. Of course, as a visitor, you would not take communion in a non-catholic church.
As an aside, if your husband's church actively preaches against the Catholic Church, you may be able to find a church where you both might be comfortable is worshipping, as visitors. Most churches welcome visitors. They are more or less pushy about changing your views. After an initial welcoming, most are happy enough to leave you alone to work out your salvation, as Paul taught.
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Many here would consider me unreasonable (not uncommon). However, I don't think that the idea of spouses attending separate church is a long-term solution within the framework of marriage. I understand that this is sometimes the best solution.
During my life, there were times when I attended two churches each weekend. There were times when I sometimes attended one church and sometimes another.
IMHO, the present issue might be to find a temporary solution. I pray that when your husband sees that your faith is important to you AND that you respect his devotion to his faith, then you might be able to take further steps. I would think that RCIA is a long way off for your husband, but that is not your concern; that is the job of the Holy Spirit.