Altera has implemented a specific protocol, different from the FTDI fast bit protocol. Also, the USB Blaster is based on FT245, that hasn't the capabilities of the newer chips. However, if you want your JTAG adapter to be compatible to USB Blaster, you would have to implement the Altera protocol somehow.
The other option is of course, to use Alter USB Blaster for your own JTAG purposes. Altera offers only a tcl interface to send JTAG commands over USB Blaster. The Altera protocol has been reverse engineered by users and can be found on the web. If you understand the protocol, you can access the USB Blaster through the FTDI driver and use it for non-Altera JTAG communication.
The third option would be to use the Altera software stack to access the USB Blaster or other Altera programming adapters by your software, but it's unfortunately undocumented. Some third party tools are using it, e.g. the Terasic Control Panel.