There will probably be arguments about whether the children should be Christened or brought up as Christians. Some couple compromise – and successful marriages generally contain plenty of that! – and give the children information about both points of view.
Atheists can marry anyone they choose as can Christians. No permission is required from any “authority” to do so. The marriage can range from living together (regarded as marriage in many countries), a civil ceremony, to full blown Catholic masses (just for the show).
If the question means can an atheist officiate at a wedding to marry another atheist to a Christian in a civil ceremony, certainly- if his authority from the local regulators of such things is in order.