Steps to create new faces between 2 selected meshes?

I have a model of a sword. In the original model, the surfaces of the flat sides of the blade are flat. I’m working to inset the surfaces a little bit to provide some depth.

I’ve separated the the model into 3 meshes, 2 for the flat parts and the third being the rest of the sword.

Now I’m trying to figure out how to join the meshes so that they create new vertical faces along the edges, but I’m not really sure how to do that. This will let me move the flat surface meshes back into place but inset a few millimeters.

Hopefully the attached screenshot will be fairly clear. I’ve selected the two edges that I’m trying to join.

After applying "Bridge Edge Loops":