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Privacy-preserving Machine Learning as a Service (MLaaS) enables the powerful cloud server to run its well-trained neural model upon the input from resource-limited client, with both of server's model parameters and client's input data protected. While computation efficiency is critical for the practical implementation of privacy-preserving MLaaS and it is inspiring to witness recent advances towards efficiency improvement, there still exists a significant performance gap to real-world applications. In general, state-of-the-art frameworks perform function-wise efficiency optimization based on specific cryptographic primitives. Although it is logical, such independent optimization for each function makes noticeable amount of expensive operations unremovable and misses the opportunity to further accelerate the performance by jointly considering privacy-preserving computation among adjacent functions. As such, we propose COIN: Conjunctive Optimization with Interleaved Nexus, which remodels mainstream computation for each function to conjunctive counterpart for composite function, with a series of united optimization strategies. Specifically, COIN jointly computes a pair of consecutive nonlinear-linear functions in the neural model by reconstructing the intermediates throughout the whole procedure, which not only eliminates the most expensive crypto operations without invoking extra encryption enabler, but also makes the online crypto complexity independent of filter size. Experimentally, COIN demonstrates 11.2x to 29.6x speedup over various function dimensions from modern networks, and 6.4x to 12x speedup on the total computation time when applied in networks with model input from small-scale CIFAR10 to large-scale ImageNet.