As far as I know, you can't do that. If one of you wanted to play single player, then you could possibly set one computer to Offline Mode before starting the game, and then the other person should be able to log in on the other account and play multiplayer, but both of you being online at the same time should not be possible.
Keep in mind, this is technically not allowed. Steam's agreement says you're not allowed to share your account or your games, that includes your fiancee. I don't think they actually do anything about it as long as you're not talking about it on steam chat or their forums. However, you still risk losing your account and all your games when bypassing their rules.
EDIT:
As of mid 2014, Steam has released Steam Family Sharing, which enables the sharing of Steam libraries. However, this system does not work on a per-title basis (only during the beta), but rather - If one title is being played, all other titles cannot be played (unless it's the same user that's using the library that is launching the second/whatever-is-after-first program).
I know of only one way that this can happen in windows, and has nothing to do with Steam other than their not-so-great decision to install all content into Program Files.
If you are on Windows 7 or Windows Vista, and you have UAC set to ON, then change it later to OFF, this can happen.
UAC does thing evil thing where if a program tries to write to a "protected" area like Program Files, EVEN IF YOU ARE ADMINISTRATOR, when you get a UAC prompt and give permission, it actually writes any files that would normally go into that directory into a "virtualized" directory somewhere else.
If you turn off UAC, that will no longer happen, and as an awesome bonus, it will no longer know about the files that it virtualized.
So in your case, if you had UAC on, installed a ton of games, then later got sick of UAC and turned it off, this would happen as you described.
See the second paragraph in "Features" in the article on User Account Control.
If you have done this and turn on UAC again, your content will come back, but be a TOTAL mess because if you've downloaded more stuff with UAC off, then that will be invisible when you turn UAC on, and vice versa.
this drove me a little crazy once before I realized what was happening.
i'm curious to know if this is your issue.
Best Answer
In the Steam client:
1) Click your username from the top right, then click 'Account Details', to go to your Steam store control page.
2) From the Steam store control page, under the 'Store & Purchase History' header, click 'View licenses and product key activations'.
This page shows, in chronological order, what games you have acquired and how (Steam store, retail code, complimentary copy, or gift). Unlike the other methods above, this activation history includes any free games you may have previously installed, but deleted.