I feel like most of the examples of heterospecific vocal communication in birds as to do more so with predator alarm calls, though are some examples for mobbing or distress calls as well -
Wheatcroft, D., & Price, T. D. (2013). Learning and signal copying facilitate communication among bird species. Proceedings of the Royal Society B: Biological Sciences, 280(1757), 20123070.
Ridley, A. R., Child, M. F., & Bell, M. B. (2007). Interspecific audience effects on the alarm-calling behaviour of a kleptoparasitic bird. Biology Letters, 3(6), 589-591.
Magrath, R. D., Pitcher, B. J., & Gardner, J. L. (2007). A mutual understanding? Interspecific responses by birds to each other's aerial alarm calls. Behavioral Ecology, 18(5), 944-951.
Hurd, C. R. (1996). Interspecific attraction to the mobbing calls of black-capped chickadees (Parus atricapillus). Behavioral Ecology and Sociobiology, 38(4), 287-292.
Fallow, P. M., & Magrath, R. D. (2010). Eavesdropping on other species: mutual interspecific understanding of urgency information in avian alarm calls. Animal Behaviour, 79(2), 411-417.
Aubin, T. (1991). Why do distress calls evoke interspecific responses? An experimental study applied to some species of birds. Behavioural Processes, 23(2), 103-111.
Fallow, P. M., Pitcher, B. J., & Magrath, R. D. (2013). Alarming features: birds use specific acoustic properties to identify heterospecific alarm calls. Proceedings of the Royal Society B: Biological Sciences, 280(1754), 20122539.
There are also a lot of great references in the online Lit Cited of this book - Interspecific Communication: Gaining Information from Heterospecific Alarm Calls (https://link.springer.com/chapter/10.1007/978-3-030-39200-0_12). I did a search for 'heterospecific' and saw 20+ papers describing this phenomenon.