Here’s the encyclical that talks about this.
vatican.va/holy_father/pius_xi/encyclicals/documents/hf_p-xi_enc_31121930_casti-connubii_en.html
The relevant section starts around number 26.
Basically, the Church definitely uses the language of the husband having authority, however, when you actually look closely at what is being said you discover that the Church’s ideal is actually essentially a model of mutual submission. I can explain more on what I mean by that and why I say that if you want.
Honestly, this is something that I don’t fully understand why the Church insists on using this language, but I take that to mean that there is some extra layer or depth to the marriage relationship that I don’t understand very well yet which is being pointed out by using this language. But I’m working on figuring it out. What I do know is that Casti Connubii makes it
very clear that the husbands authority over his wife is not a universal one-sided dominance, that it is wrong to think this order comes from some defect in women’s ability to think or reason, that there are times when it is a wifes duty to stand up to her husband and take his authority, and that the ideal order of a man’s authority over his wife will look different in different households depending on many factors, including the people, place and time (In other words the form of authority will change depending on the people and their particular strengths and weaknesses as well as the culture they live in). When you take into account that the Church’s teaching on the husband’s role actually is, that he must lead by serving and by sacrificing every aspect of himself for his wife, it becomes pretty aparant that while the Church uses this language of the husband having authority over his wife it very clearly does not mean it as the domineering or universal and complete authority many people take it to mean.
I hope that is helpful.