[edited]Yes all that is necessary is that the parents be able to assure the priest that they will do all in their power to raise the children Catholic and educate them in the Faith. Your husband and the godparents--who also must be Catholic--will probably be required, and you will be invited, to attend some type of preparation class on the sacrament itself and what it means for Catholics, and on your obligations. Please contact your husband's parish to find out what the procedure is in your area.
These classes, and those offered when your children prepare for the other sacraments, can be very instructive and helpful for you as the non-Catholic parent in understanding what they learn and do, and appreciating the similarities and differences to your own faith. You already have a difficult task coping with one potential source of conflict in the family, so anything that aids communication and understanding is to the good. You may find in time, and I see this a lot, that you may be even more faithful than your Catholic spouse in taking care of your child's religious education so I would like to take this chance to thank you and all non-Catholic parents of Catholic children who do take this responsibility seriously, you are a blessing and a credit to your own upbringing.