Hey there! I'm a Sc/BMS double degree student who just finished their first year at Monash. What Sine said about electives is correct - your only 'electives' must be science related.
If you're considering this double, make sure you're not doing science to do a biomed related major (such as biochemistry or physiology) - you're not allowed to (although the you can still do some of the units). If you're interested in doing a language or an arts major on top of the double, you can do a diploma, which takes about an extra year.
The opportunities that you can get out of doing science will depend on what major you decide to pursue. In my opinion, there is no significant benefit in doing the double if your end goal is to apply for grad med at Monash, since biomed alone will suffice all the requirements.
Hope this helps 
Thanks for your reply.
If you don't mind me asking, what are you planning to major in for your science degree? Which subjects did you do this year?
Also, do you also know if it is possible to commence a BSc double degree or any other double degree program with the BBioMedSci following your commencement of a BBioMedSci degree?
I am mostly interested in human biology (e.g. immunology, physiology), Biochemistry and public health policy to some extent based on what I have been doing at high school. If Med (either at Monash, Unimelb or interstate) doesn't work out after my undergraduate degree, I might apply to allied health (dentistry, optometry, imaging etc.) or go into academic research with an MSci or honours year and PhD. Do you know if there are significant prospects for commercial employment for graduates in Biomedical Sciences (e.g. in biomedical start ups)?
I am also thinking of taking up French again at university as I stopped doing at Year 10 as it was quite risky to take French into VCE given my skill level. I might look into the Diploma as you suggested and do that if French proves to capture my interest.
Again, thanks for all you advice.
