Hi!
I do not know if the interviewer had a lot of knowledge or it was just trying to confuse you, however please be aware that I consider your L2 VLAN answer partially correct (I will take it as correct in an interview).
VLAN is a technology which defines broadcast domains in a layer 2 network. There is no such a thing as a L3 VLAN.
Please refer to the following documentation for actual detail definition of it:
http://www.cisco.com/c/en/us/td/docs/switches/lan/catalyst4500/12-2/25ew/configuration/guide/conf/vlans.html
VLANs define broadcast domains in a Layer 2 network. A broadcast domain is the set of all devices that will receive broadcast frames originating from any device within the set.
Hope it helps, best regards!
JC