Based on the fact that it is a major American Bank (assuming they have a big presence in Sg), and what you have described about your portfolio, your position sound pretty senior.
In excess to the SGD180K, are they providing other things, i.e. paying for your apartment, car, etc? If you havent sign the line, i think you have a good chance trying to negotiate for a better deal...
From what i understand, different banks offer different kind of benefits & compensation package. Some are more skewed towards more benefits (i.e. lodging, car, country club membership, etc) and i know some offer very minimum benefits but offer a higher compensation package. Dont be shy to drill your HR for more information, and ask for more things. If you dont ask, you wont get alot of things. Dont assume that they will tell you everything...HR is rarely the most helpful people.
As for your partner's situation, i might not be the best person to ask. I know that NUS (a local and very reputable university) offers medical course. You can call and check if they are able to continue her studies and/or do her residency in Singapore. If they are not able to let her continue her studies, they should be able to point you to the right direction.
http://www.med.nus.edu.sg/corporate/