Is it possible to backup an iPhone to both iCloud and iTunes?
Yes, this is possible.

The options you're referring to in iTunes relate to automatic backups. You can achieve what you want by enabling iCloud backups (either in iTunes or in your iPhone's settings) and then manually doing a backup to iTunes whenever you want. 

To do a manual backup to iTunes, simply connect the iPhone as you usually do with iTunes and then in the device's Summary screen within iTunes (the one with the backup options) you'll see to the right a Back Up Now button. Just click this whenever you want to also backup to iTunes.