Is it possible to use npm to run scripts in multiple subfolders?

You can use concurrently to accomplish this. So you would create a package.json which looks something like the following:

...
"scripts": {
  "client": "cd client && npm start",
  "server": "cd server && npm start",
  "assets": "cd assets && ionic serve",
  "start": "concurrently \"npm run client\" \"npm run server\" \"npm run assets\" ",
},
...
"devDependencies": {
  "concurrently": "^1.0.0"
}
...

Note: This will start all three processes concurrently which means that you get mixed output of all three (like @topheman already mentioned)