He wanted to be a dad and taking care of Angel was his way of being involved in the whole process. If by any small chance Ben couldn't be there when the babies were born Denzel would be.
Kari didn't want children right away, she wanted to wait at least a year -at the very least! He hadn't been very happy about that but, he had agreed to wait a year. Then Evangeline was pregnant and it didn't matter so much that Kari wanted to wait. Sometimes, once or twice Angel had allowed him to touch her belly and feel the babies move . They were a lively bunch and for the time he was allowed it was the next best thing to them being his own. In actuality, sometimes he would pretend that it was his family.