I breed chickens, and quite frequently have a hen and rooster pair housed together. I have noticed that when there is only one hen, the rooster is usually much more friendly to the hen, and tends not to rough her up so much.
However, there are breed differences. For breeds that raise their own chicks, the rooster and hen tend to get along better as a pair instead of with one roo and multiple hens. Breeding setters tends to work better with pairs than with trios. Inevitably, one hen starts to set before the other,. So eggs are laid after the start of the brooding. The later eggs don't hatch with the rest, so either you give them up or finish them in an incubator and sneak them back under the hen at night.
And there are also individual bird personality differences.
If you are introducing them, side by side cages or a divided cage for a few days will help the rooster and hen get along better once you let them get together. And you will want to check his spurs and claws to make sure they aren't too long or sharp when you put them together.
From the picture, I guess they are a white leghorn and a cuckoo Maran.
