Or does each person have to do it?

It depends on the circumstances - in my area an entire family cannot be covered by one order. There might be one hearing, but there are separate orders.

As Judy said we need to know what is going on first. In the case of adults in the family then they will have to seek their own order from the court. For minor children then they may be covered as far as you making the application for a restraining order.

The question was whether OP can "file a restraing order"; "Or does each person have to do it?

One does not file an order; one files an application for an order. Then, hopefully, a judge signs the order.

To answer the question, OP would file single application for an order, such order perhaps protecting OP and other members of OP's family.

I agree with the correction - the OP can request an order. The Judge will (or won't) grant it.

However, I've been in this position. Each adult in NY files for the protective order and it is granted (or not) based on THAT individual's experience with the other person. The fact that the person harasses me and I need protection does not mean that my husband does.

The children fall under either husband or wife.

In NY it is not one order for the entire family.

When a person is home one party's protective order, of course, cloaks everyone, same when the family is out as a group. However, if I have the order and my husband runs into the other person, that's another story.