My file structure would look something like:
./client
.react
./server
.express
.express and .react are just shorthand for all of my files in these folders. So I have separate node_modules folders for each of these directories.
I wouldn't do it with npm itself. It might be handy to create a Makefile in the root, running your required build steps.
This article explains how to create a Makefile.
This same happen to me when I worked on the good solution is to make top level on these two workspaces. Just visit the given url workspaces you will get the idea how to manage that kind of flow and single top level package.json