Many linear time-varying (LTV) channels of interest can be well-modeled by a multi-scale multi-lag (MSML) assumption, especially when wideband transmissions with a large bandwidth/carrier-frequency ratio are employed. In this paper, communications over wideband MSML channels are considered, where conventional communication methods often fail. A new parameterized data model is proposed, where the continuous MSML channel is approximated by discrete channel coefficients. It is argued that this parameterized data model is always subject to discretization errors in the baseband. However, by designing the transmit/receive pulse intelligently and imposing a multi-branch structure on the receiver, one can eliminate the impact of the discretization errors on equalization. In addition, to enhance the bandwidth efficiency, a novel multi-layer transmit signaling is proposed, which is characterized by multiple data rates on different layers. The inter-layer interference, induced by the multi-layer transmitter, can also be minimized by the same design of the transmit/receive pulse. As a result, the effective channel experienced by the receiver can be described by a block diagonal matrix, with each diagonal block being strictly banded. Such a channel matrix structure enables the use of several existing low-complexity equalizers viable.