When talking about parents and their own children, 'bring up' and 'raise' have the same meaning. 'Raise' is used mainly in American English, while speakers of British English tend to say 'bring up'. 'Foster' has a completely different meaning. If you foster children you care for children in your home for a period of time. These children may be orphans, or they may have parents who are either unable or not allowed to look after them. 'Foster parents' look after children for anything from a few weeks to several years. This can be a business arrangement. The state/social services often pay foster parents to look after children who are in state care for whatever reason. For many foster parents, this is a career or at least a part-time job.

You would use "raise". Foster implies that the children are not theirs, bring up is just awkward.

I think raise is correct.