Hmmm.
A double degree is an option.
You can do Arts/Science as some have suggested which gives you a bit of a taste in both areas. I know you're a bit anti-Monash, but I travel pretty far to Monash and even though I'm not doing a double degree, if you're more likely to travel that extra bit further then chances are you'll probably stay a bit longer and do some actual study rather than gallop off shopping or whatever if you've got that sort of temptation...(shush, I'm female!)
I honestly haven't looked much into how double degrees work, but I know that there are some universities where you can do 2 units from each faculty in the same year at the same time, such as 2 Arts and 2 Science. But then apparently other Unis make you do all Science, then alternate or something like that. A girl in my French stream is doing Arts/Education, so basically all the content she learns in Arts she immediately is learning how to implement it in the classroom. Thought that was pretty nifty. And pretty sure a double degree would lengthen your course duration by a year.
I can fully understand your concerns about future career prospects. I know at Monash that you can select to study a sequence (or Breath, whatever) from another faculty such as doing Marketing from commerce/business. There's opportunity to customise that degree of yours.
Personally, I'm doing Arts: Linguistics, French, Sociology & Journalism. I hope to major in Linguistics, but I've Journalism stuck in there too for something more concrete to focus on in the workforce. I personally would love to be doing Psychology though. At the moment I've got French and Sociology that I'm quite interested in, but now that I've got a passion for Linguistics I can now drop them, do a double major in Ling, pick up Behavioural studies, Psychology, etc - the possibilities are endless. That's the beauty of Arts - practically no set rules about how to structure your degree.
So I spose if you're deciding between Bach Science vs Arts, I'd go with where your passions are. Talk to teachers, past and current students, currently employed Psychologists, go to Open Days in August and read the Uni websites for all their information on courses and units!