Yes, but the Anglican is required by the Catholic church to accept that any children will be brought up as Catholics and the Catholic is required to endeavour to bring the Anglican into the Catholic church. Consult your priest for further info.

You can seek the approval from the Priest in charge of the individual church, and depending on the degree of orthodoxy, he may approve it. You'll likely be asked to attend CCC classes or convert.

Here is an answer I posted to another question, but the answer is the same. This is allowed, with words of caution that it may be difficult. Also, the Catholic must be sure to keep their own faith and baptize and raise the children Catholic. See below for exact wording. (The ...'s are where I removed stuff in reference to Catholic/Non Christian marriages) From the Catechism of the Catholic Church: #1634 "Difference of confession between the spouses does not constitute an insurmountable obstacle for marriage, when they succeed in placing in common what they have received from their respective communities, and learn from each other the way in which each lives in fidelity to Christ. But the difficulties of mixed marriages must not be underestimated. They arise from the fact that the seperation of Christians has not yet been overcome. The spouses risk experiencing the tragedy of Christian disunity even in the heart of their own home...Differences about faith and the very notion of marriage, but also different religious mentalities, can become sources of tension in marriage, expecially as regards the education of children. The temptation to religious indifference can then arise." #1635 "According to the law in force in the Latin Church, a mixed marriage needs for liceity the express permission of ecclesiastical authority...This permission presupposes that both parties know and do not exclude the essential ends and properties of marriage; and furthermore that the Catholic party confirms the obligations, which have been made known to the non-Catholic party, of preserving his or her own faith and ensuring the baptism and education of the children in the Catholic Church."