Father should consider filing a complaint for custody to gain visitation rights. Although the couple is separated, that separation does not terminate father's parental rights. Parental rights can be terminated involuntarily (when there is cause or reason to have such rights terminated) or voluntarily (that is, with consent of the father).
Based on your question, father wants to be involved in his children's lives. Accordingly, I recommend that father contact a family law lawyer in his jurisdiction, especially one specializing in custody, in order to pursue his custody/visitation rights.
Answered on Feb 17th, 2015 at 7:04 PM