You can think of a convertible bond as a bond, with an option on the stock. So the bond may be worth $100, and the option to buy the stock might be worth $20. Since convertible bonds aren't liquid, and the implied option may be hard to short, the $120 combined price is really just theoretical. If the convert trades at $110, then the buyer will buy the convert, and then try to short the debt (either shorting another bond from the same company, or with CDS), shorting some amount of stock (Perhaps a half share per option calculated with Black-Sholes or another option pricing method, or perhaps going short a similar option).

Does this make sense? If not, I can try to write it in more clear English.