We present the context-unified encoding (CUE) model, a large-scale spiking neural network model of human memory. It combines and integrates activity-based short-term memory with weight-based long-term memory. The implementation with spiking neurons ensures biological plausibility and allows for predictions on the neural level. At the same time, the model produces behavioral outputs that have been matched to human data from serial and free recall experiments. In particular, well-known results such as primacy, recency, transposition error gradients, and forward recall bias have been reproduced with good quantitative matches. Additionally, the model accounts for the Hebb repetition effect. The CUE model combines and extends the ordinal serial encoding (OSE) model, a spiking neuron model of short-term memory, and the temporal context model (TCM), a mathematical memory model matching free recall data. To implement the modification of the required association matrices, a novel learning rule, the association matrix learning rule (AML), is derived that allows for one-shot learning without catastrophic forgetting. Its biological plausibility is discussed and it is shown that it accounts for changes in neural firing observed in human recordings from an association learning experiment.