ばかりでなく is a combination of the 副助詞（ふくじょし） (adverbial particle) ばかり, with the conjugated (and negated) form of the 助動詞（じょどうし） (auxiliary verb) だ. It can be translated as ‘not only (A), (B)’, or ‘not limited to (A), (B).
As ばかり is a 副助詞（ふくじょし）, it may be paired with the 連体形（れんたいけい） (attributive form) of other words.

• 彼（かれ）は仕事（しごと）ばかりではなく、家事（かじ）もちゃんとやっています。
  Not only does he work, but he does house chores too.
• 都内（とない）にある安（やす）いアパートは古（ふる）いばかりではなく、だいたい小（ちい）さくて汚（きたな）い。
  Cheap apartments in metropolitan areas aren't only old, but they are usually small and dirty.
• この池（いけ）は綺麗（きれい）なばかりではなく、ワニが沢山（たくさん）いるので危（あぶ）ないです。
  This lake is more than just beautiful, there are a lot of alligators, so it is dangerous too.
• 彼（かれ）は宝（たから）くじに当（あ）たって、車（くるま）ばかりではなく、ボートとバイクも買（か）った。
  He won the lottery, and not only did he buy a car, but he also bought a bike and a boat.

Like all other grammar points that negate だ, several forms may be seen. でなく, でなくて, ではなく, ではなくて, じゃなく, じゃなくて. However, it is important to remember that the addition of the は particle will place further emphasis on ない.