You're absolutely right; domestic violence isn't only men abusing women. It can take many forms; women abusing men, children abusing parents, women abusing other women, etc. etc., and in some cases, it can be very hard to determine who is the victim, and who is the perpetrator; couples can be abusive towards each other, although there is often one partner who is worse than the other. I hear the about some of these cases from my partner, and the one thing that can be said is that domestic violence situations are often complicated.
However, you are also absolutely wrong about not knowing the relative incidence - violence against women perpetrated by men is much more common than the other way around. There is a stigma against men reporting violence in abusive relationships, but even when this is taken into account, all indications are that men hit women more than women hit men.
Historically violence against men has been under-reported to a greater extent than violence against women. We are now getting closer to a situation where the stigma does not exist, but there is some way to go yet. Society (wrongly) expects men to be 'tough', and women 'soft'. Such crimes often go unreported for a number of reasons, no only the stigma, but also out of fear of retribution, people turning a blind eye, and other more complex reasons. In a humane society, we should be encouraging victims of abuse to come forward, and supporting them in doing so; there are several very worthy charities which provide support and shelter for abused women (and also men). I'd encourage everyone to do what they can to support them.