The root raised-cosine pulse commonly used in linear digital modulations yields exactly two intersymbol interference components from the preceding and the subsequent data symbols, provided that the roll-off factor is $100\%$ and the modulation packing factor is set to $50\%$. This can be exploited to symmetrically multiplex two data streams of transmitted symbols. Hence, the proposed scheme is referred to as pulse-shape binary multiplex modulation. The demodulation of the two multiplexed data streams at the receiver can be aided by making the streams mutually orthogonal. It can be achieved by superposition modulation with symbol-by-symbol interference cancellation, proper design of transmission sequences interleaving pilot and data symbols in order to also enable channel estimation, and using orthogonal spreading sequences. The presented numerical results indicate that the proposed modulation scheme can outperform Nyquist signaling in terms of transmission reliability or the time required for transmitting the whole sequence of data symbols. For instance, differentially encoded modulation symbols can be transmitted twice as fast by the proposed modulation scheme with a 3 dB penalty in signal-to-noise ratio over additive white Gaussian noise channels.