So you have two independent legal Broadband accounts (can be two DSL two Cable or one of each.)
There are two terms that might be associated with using two independent Internet connections.
Combining Bandwidth.
Load Balancing two connections.
Let assume that you have two 3Mb/sec. connections each capable to download at 300KB/sec.
With Combined Bandwidth you should be able to download one file at 600KB/sec.
With Load Balancing one single file will not exceed download speed of 300KB/sec. However you can download 2 files at 300KB/sec. or 4 files at 150KB/sec. etc.
Unfortunately Combining Bandwidth can not be done without the ISP providing such a specific service.
Computers are Not mind readers. If the two connections are not synchronized at the source your computer would know how to combine it to a coherent page.
Any if and but about it is just Wishful thinking.
The price of such a service (if available) is usually much more expensive than upgrading your connection from the basic service to a faster business or corporate service.
If you do have two independent services you can achieve Load Balancing by using a Dual WAN Router.
This type of Cable/DSL Routers have two WAN connections for two Broadband Modems and they would mange the Internet traffic to the LAN to be used in the most efficient way.