Scripture is pretty clear on who is the Spiritual head of the family (house). Even if one is dating the man needs to be the Spiritual head of the relationship and both need to be evenly yoked. It doesn't mean he dominates the women, but that both are on mutual grounds.
Eph 5:22 Wives, submit yourselves unto your own husbands, as unto the Lord.
Eph 5:23 For the husband is the head of the wife, even as Christ is the head of the church: and he is the saviour of the body.
Eph 5:24 Therefore as the church is subject unto Christ, so let the wives be to their own husbands in every thing.
Eph 5:25 Husbands, love your wives, even as Christ also loved the church, and gave himself for it;
2Co 6:14 Be ye not unequally yoked together with unbelievers: for what fellowship hath righteousness with unrighteousness? and what communion hath light with darkness?