I'm about to starting taking antabuse (disulfiram) tablets to get rid of my drinking habbit. Can I continue smoking?

Yes. Antibuse should not interfere or make you sick if you continue smoking.
Doesnt get rid of it. Antabuse (disulfiram) is the least effective of the agents approved to help people stop drinking, mainly because people don't take it regularly. However, alcohol problems are caused by issues in a person's life, and if you don't get counseling to deal with these issues, it is unlikely that, even if you quit, you will stay quit. To answer the main question, you can smoke without interfering with the antabuse (disulfiram).