The Bible never says that a man is the priest of the home, all Christians are part of the priesthood of believers. A priest is one who has a certain level a access to God. In the OT priests were designated to perform certain ceremonies and sacrifices. Priests were the only ones allowed to access certain parts of the temple. After Christ rose again all believers have equal access to God through Jesus Christ.
However a husband does have specific roles in the marriage and family.
Ephesians 5:
22: Wives, submit yourselves unto your own husbands, as unto the Lord.
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.
24: Therefore as the church is subject unto Christ, so let the wives be to their own husbands in every thing.
25: Husbands, love your wives, even as Christ also loved the church, and gave himself for it;
26: That he might sanctify and cleanse it with the washing of water by the word,
27: That he might present it to himself a glorious church, not having spot, or wrinkle, or any such thing; but that it should be holy and without blemish.
28: So ought men to love their wives as their own bodies. He that loveth his wife loveth himself.
29: For no man ever yet hated his own flesh; but nourisheth and cherisheth it, even as the Lord the church:
30: For we are members of his body, of his flesh, and of his bones.
31: For this cause shall a man leave his father and mother, and shall be joined unto his wife, and they two shall be one flesh.
32: This is a great mystery: but I speak concerning Christ and the church.
33: Nevertheless let every one of you in particular so love his wife even as himself; and the wife see that she reverence her husband.
The man is to be head of the church as Christ is the head of the church. This gives a husband authority over his wife. But a man is to love his wife as Christ loved the church. So in all the ways that Christ loved the church we must do our best to love our wives in the same manner. How did Christ love the church, by teaching the word of God, by providing for physical needs, by rebuking and correcting when need, and by placing the needs of others over himself. These are some of the examples that I can think of.
Colossians 3:
18: Wives, submit yourselves unto your own husbands, as it is fit in the Lord.
19: Husbands, love your wives, and be not bitter against them.
1 Peter 3:
5: For after this manner in the old time the holy women also, who trusted in God, adorned themselves, being in subjection unto their own husbands:
6: Even as Sara obeyed Abraham, calling him lord: whose daughters ye are, as long as ye do well, and are not afraid with any amazement.
7: Likewise, ye husbands, dwell with them according to knowledge, giving honour unto the wife, as unto the weaker vessel, and as being heirs together of the grace of life; that your prayers be not hindered.
Men are required to take the leadership role in the marriage and family but is it not the role of a priest.