I can only really add to the answers previopusly given.
As far as simply viewing pornography, there is unlikely to be any seerious issues here legally - the powers-that-be are really only interested in people who download material - i.e. save it to a computer hard-drive for collection or dosemination, and that is normally confined to the more serious end of the system - as already delineated by previous correspondents.
However, I do think you have a serious issue with the fact that your partner is showing blatent disregard for you as his partner, and for your children. That is less about whaty he actually looks agt, than the fact that he appears indifferent to his responsibilities to you as his partner, and to your children.
I think you need to have a serious talk with him, not in the area of pornography, but about his attitude to you and the children, and his relationship with you. That to me is the serious matter here.