Basically, for both of you couples there is no BF/GF pass. If you have a marriage certificate and/or evidence of a common law marriage, then you can be issued a dependent or a long term social visit pass. Otherwise you will only be allowed a 30 days visitors pass from the UK, 90 days from the US and Australia.
Options - you leave the country and come back when your social pass is about to expire. To get 30 days, it must be on an airplane (so I understand)... a bus trip to Malaysia will only get you 14 days. You can do this for about a year before your pass will no longer be renewed.
If your BF/GF's employer is helping, then that means they are applying for some sort of employment pass for you. There are no other passes.
You could consider applying for landed PR status if you intend on staying here permanently, have college degree or better, and multiple years of professional experience, but this is not easy to get.
MoM website:
http://www.mom.gov.sg/MOM/CDA/0,1858,96 ... --,00.html