Does a database backup include all files? If I have two files in my database (mdf &amp; ndf), when I do a backup of the database with the statement:

backup database mydb;


are both the two files are backed up?
Yes. Details here: Backup Overview (SQL Server)

This is the section relevant for you: 


Full backup

A full backup contains all the data in a specific database or set of filegroups or files, and also enough log to allow for recovering that data.


You should always test the backup (ideally by performing a restore to another location) to ensure you can recover your data in the event of a disaster.