How can I get my android emulator use my computer's VPN interface?

First start your vpn connection and then restart the emulator, now the emulator should use the host vpn connection.

it's mostly because of the DNS issue, according to the android doc:

At startup, the emulator reads the list of DNS servers that your system is currently using. It then stores the IP addresses of up to four servers on this list and sets up aliases to them on the emulated addresses 10.0.2.3, 10.0.2.4, 10.0.2.5 and 10.0.2.6 as needed.

What I do on my mac is just make sure 'send all traffic over vpn' is checked. You'll find this setting after you click advanced while having your vpn connection selected in network preferences.

Works well for my situation, but may not depending on the type of VPN you're connecting to.