Is the Bible misogynistic?

First, let me say that it is important to define terms when having discussions about contentious issues. Today I’d like to discuss a contentious issue. I’ll start by defining terms.

Misogyny: dislike of, contempt for, or ingrained prejudice against women.
Misogynistic: strongly prejudiced against women.
Ingrained: (of a habit, belief, or attitude) firmly fixed or established; difficult to change.
Prejudice: an unfair and unreasonable opinion or feeling, especially when formed without enough thought or knowledge

So, putting some of that together, the question that forms the title of this OP boils down to this:

Does the Bible contain a firmly fixed, unfair and unreasonable opinion with regards to women?

I offer for your consideration the following quotation (although I do not say that it is the only, or even the worst, example):

Wives, submit yourselves to your own husbands as you do to the Lord.
For the husband is the head of the wife as Christ is the head of the church, his body, of which he is the Savior.
Now as the church submits to Christ, so also wives should submit to their husbands in everything.

I could go off on a tangent from the main theme about how the law in my [Christian] country of birth, at the time of my birth, did not recognise even the possibility of marital rape, and how I suspect that the Bible had some part to play in that. However, that is a diversion from the main topic.

I feel sure that if I don’t mention that the very next verse following the one I’ve quoted above does urge that men should love their wives, many folk will accuse me of cherry-picking, but I would point out that it absolutely says nothing about husbands having to be obedient to their wives.

So… here we are. Questions for consideration:

Is it fair and reasonable that a wife should have to obey her husband in all things, but that he should have no such obligation to her?
Is the Bible misogynistic?