How to cut a lengthways section from a 2x4... without a table saw?

So we had some damage here in Ireland from Storm Éowyn and I need to make new doors for our summer house in the garden. I'll need some 2x4s cut like this, this is the cross section and I want to remove the shaded area. (It's the inset where the glass panels rest).

I have a mitre saw which is no good for this and a jigsaw... Can I get away with clamping bits of wood together and trying to get the jigsaw to cut it?

I don't really have room for a table saw. Is there another way to do this?