We introduce a novel hybrid failure model, which facilitates an accurate and detailed analysis of round-based synchronous, partially synchronous and asynchronous distributed algorithms under both process and link failures. Its utility and expressiveness is demonstrated by means of a complete analysis of the well-known randomized Byzantine agreement algorithm of (Srikanth & Toueg 1987). Granting every process in the system up to l link failures (with la arbitrary faulty ones among those) in every round, without being considered faulty, we show that this algorithm needs just n >= 4*l+ 2*la +3*fa +1$ processes for tolerating fa Byzantine process failures. The probability of disagreement after R iterations is only 1/2^R, which is the same as in the FLP model and thus much smaller than the lower bound O(1/R) known for synchronous systems with lossy links. We also provide a detailed analysis of the algorithm's running time, as well as an evaluation of the model's assumption coverage in systems with transient link failures. Finally, stubborn links are shown to be sufficient for this algorithm. In accordance with our findings for synchronous systems obtained elsewhere, our results reveal that randomized Byzantine agreement can be solved efficiently even in asynchronous systems with imperfect communications. Contrasting widespread believe, there is no need to employ a perfect communications subsystem even in case of excessive link failure rates.