Ah, I thought as much from your original post. Your problem is a little something called contention.
Think of your internet connection as a motorway (or freeway, autobahn, whatever you call them where your from) and the data you are transferring as the cars. It can only physically take so much traffic. When traffic is light all car's (and data) move at the optimum speed.
This works fine, right up until the point where the number of car's exceeds the number of cars that can travel on the motorway at optimum speed. At this point, everyone is forced to slow down.
What's basically happening, is your internet connection can only handle so much data at a time (depending on bandwidth). Online games actually need very little bandwidth, ping time (response time from the server) is far more important. This is why the problem doesn't manifest while one of you is gaming.
When you are downloading something, it will try to fill all the available bandwidth, (assuming the server can deliver it that fast). When two of you are downloading, you still have the same amount of bandwidth, but it is now being spread between two machines.
So for example: I have an 8Mb/s connection. After overheads, and translating bits (which internet speed is measured in) to Bytes (which download speed is measuring) this translates to about 900KB/s (this is in an ideal world, in reality it can be anywhere between 700-850 depending on all sorts of conditions... but I will keep it simple)
So, lets say I start a download from a big site, like Nvidia. To start off with, I'm getting all 900KB/s of goodness, but what happens if my girlfriend decides that she absolutely has to download something? Well then my connection is being split between two machines, sure there is still 900KB/s of bandwidth available, but now it isn't just going to me, it's being split between us.
Here's the rub though. The split isn't even, the two connections will "fight" each other, trying to get more bandwidth. So in my example above, rather than getting 450KB/s each, it's more likely our download speeds will vary from 300KB/S anything up to 600KB/s as the fight goes back and forth. Obviously downloading is a lot more bandwidth intensive than merely browsing web pages. In that situation the web pages invariably lose out, causing a slowdown or lag while waiting for responses.
We call this contention, because the connections are fighting, or contending, with each other.
Effectively there is nothing you can do about it, the slow down is going to happen either way, the only way to at least offset the problem is to upgrade your internet package. Contention will still happen though, it's just the speeds your fighting for will have more bandwidth available.
Another thing to consider is upload speed, as counterintuitive as this sounds, in order to download, you have to upload. Basically, for every x amount of data received your PC has to send an "ack" packet that tells the site it has got it, whereby the site will then send the next x amount of data. If all your upload speed is being used, contention comes in again. It is much easier to clog the upload than the download, as most connections have a much lower upload bandwidth.
I hope this helps, if you have any questions please feel free to ask, and I will answer the best I can.