Your husband is alluding to St. Paul’s exhortation in his Letter to the Ephesians:
21 Be subject to one another out of reverence for Christ. 22 Wives, be subject to your husbands, as to the Lord. 23 For the husband is the head of the wife as Christ is the head of the church, his body, and is himself its Savior. 24 As the church is subject to Christ, so let wives also be subject in everything to their husbands. 25 Husbands, love your wives, as Christ loved the church and gave himself up for her, 26 that he might sanctify her, having cleansed her by the washing of water with the word, 27 that he might present the church to himself in splendor, without spot or wrinkle or any such thing, that she might be holy and without blemish (Ephesians 5:21-27).
Is your husband asking you to attend his religious service in place of your participating in Sunday Mass? If so, charitably tell him that your first obligation is to Jesus Christ (Matt. 6:33), and so you must be faithful to Christ and the Church he established (Matt. 16.18-19), and that you will thereby be a better wife and mother, if you have any children, as a result.
So participating in his religious service at the expense of your Sunday Mass obligation is non-negotiable, charitably share with him, because it would be a violation of the Third Commandment. (He might view it as the Fourth Commandment, based on a Protestant numbering of the Decalogue.)
Is he asking you to attend his service in addition to fulfilling your Sunday obligation? If so, that’s something to consider to promote marital harmony, provided you aren’t subject to coercive efforts by members of his congregation to leave the Catholic Church and his pastor is at least generally respectful of Catholics as Christians, so you don’t have to endure anti-Catholic sermons regularly. In addition, charitably explain to your husband that you cannot receive communion at his church because it would imply a full unity and solidarity in faith that unfortunately doesn’t yet exist between you and his congregation.
So I would recommend participating in Sunday religious service if possible, although charitably explain to him that other obligations may preclude you from always participating in both Sunday Mass and his religious service.
In addition, if you’re not doing so already, I would encourage you to pray as a couple every day, even if only for a short period of time. That will bring you closer to each other in the Lord and help you to better know and appreciate each other’s needs and struggles. As Father Patrick Peyton used to say, “The family that prays together stays together.”
Finally, as St. Paul says in Ephesians 5, your husband is called to love you as Christ loved the Church, which means laying down his life for you (Eph. 5:25). A wife is always more likely to follow her husband’s lead if she can see by his daily actions that he really loves her and so doesn’t attempt to lord his leadership over her. Rather, he should discuss with his wife all family matters, respecting her input and deferring to her whenever possible.