This paper presents an asymptotic analysis of multisignature code-division multiple access (CDMA) in the presence of frequency-selective channels. We characterize the sum spectral efficiency and spectral efficiency regions for both the optimal and linear minimum mean-squared error (MMSE) multiuser receivers. Both independent and identically distributed (i.i.d). signatures and isometric signatures, which are orthogonal at each transmitter, are considered. Our results are asymptotic as the number of signatures per user and processing gain both tend to infinity with fixed ratio. The spectral efficiency of the MMSE receiver is determined from the asymptotic output signal-to-interference-plus noise ratio (SINR). For isometric signatures, our results rely on approximating certain covariance matrices with unitarily invariant matrices that are asymptotically free. This approximation is shown to be very accurate through comparison with both simulation and an "incremental-signature" analysis, which can be used to compute asymptotic moments. Also, a novel proof of the convergence of the empirical spectral distribution of the signal correlation matrix is presented. From these results, we derive the optimal coding-spreading tradeoff, which maximizes the MMSE spectral efficiency, for the case of a single user with multiple i.i.d. signatures. Simulation studies demonstrate that the asymptotic results accurately predict the performance of finite-size systems of interest. The resulting expressions are used to highlight and infer properties of the multisignature CDMA system, including the benefit of orthogonal relative to i.i.d. signatures, and the tradeoff between spectral efficiency and the versatility of providing a variable data rate service through multiple signatures