Most previous work in statistical multiplexing only considered the case where the link transmission rates are fixed. In this paper, we consider statistical multiplexing in networks with adaptive transmission rates, with focus on DSL broadband access networks. This requires a jointly optimized allocation of buffer space and transmission bandwidth to traffic flows, which takes the flow traffic characteristics, the user QoS requirements, and the user interactions at the physical layer into consideration. Using the Effective Bandwidth concept, we propose a class of Alternate Maximization (AM) algorithms (AM-D and AM-M), which solve the statistical multiplexing problem for both delay insensitive Data traffic and delay sensitive Multimedia traffic. With low complexity as a design goal, the AM algorithms incorporate our recently proposed Autonomous Spectrum Balancing (ASB) algorithm, which was originally designed for DSL physical layer spectrum management. Our numerical results show that the AM algorithms combines the gain due to statistical multiplexing and that due to spectrum management.