The scene that you are describing is when the first chaos is occurring that eventually leads to the mass destruction of mankind. Both the wife and her husband didn't really know what was going on; they were confused and a bit alarmed. They got out of bed, and tried turning the lights on, but they didn't turn on; the electricity was already gone. The father, realizing that they didn't have power, probably wondered if the water lines were damaged, or if the pipes had been hit. So, he went to the bathtub and turned on the faucets "on both taps as far as they would go." He was probably just checking to see if they still had functioning water. Why? The power was off, they had seen fire and heard rattling like a bomb or a major impact of something, so he was probably worried that the damage was more extensive than just the power.
It never directly states any of this in the novel--this is one of those situations where you have to infer, or use an educated guess to read in-between the lines. It only makes sense that the father would be concerned about their safety and resources. His wife, confused, asks, "Why are you taking a bath?" and he says that he isn't, and that is all that the book tells us, so inference is the way to kind-of guess what he might be doing. I hope that helped; good luck!
That is a good question, especially because the movie does not really give an explanation. I think that there are two explanations for this. First, as you say, they see fire. This is probably the first reason. The best thing to combat fire or one of the best things, is water. So, the husband is probably getting water to protect themselves. Also, water is something essential to live. So, they are also getting water to store up. They do not know how bad the disaster is, but they can guess that is is pretty bad. I would probably do the same thing.
The mother and father are witnessing a nuclear disaster. The father is running water into the tub to provide them with a safe water supply. Water in the pipes will not have radiation contamination from nuclear fallout.
When I first read it I thought he might realise that with the power going off and because of the context of the events to the man that he was worried about water. That he realised that water might become a scarce resource, especially purified water from a tap.