Is sexual reproduction outside the same biological family possible? Has it ever occured successfully?
Interfamilial hybrids have never, to my knowledge, been recorded occurring naturally (without human intervention).

In plants, somatic inter-familial hybrids have been produced for a wide variety of species pairs in the lab (e.g. between carrot and barley; Kisaka et al. 1997). 

In animals, there are some historical reports of hybrids between chickens (Mathis &amp; MacDougald 1987) or peafowl (Serebrovsky 1929), both in Phasianidae, and guineafowl (in Numididae). The animal example meets your condition of being outside the lab, although they were produced by breeders.

Refs


Kisaka, H., Kisaka, M., Kanno, A. &amp; Kameya, T. (1997) Production and analysis of plants that are somatic hybrids of barley (Hordeum vulgare L.) and carrot (Daucus carota L.). TAG Theoretical and Applied Genetics. 94 (2), 221–226.
Mathis, G.F. &amp; McDougald, L.R. (1987) Evaluation of interspecific hybrids of the chicken, guinea fowl, and Japanese quail for innate resistance to coccidia. Avian Diseases. 31 (4), 740–745.
Serebrovsky, A. (1929) Observations on interspecific hybrids of the fowl. Journal of Genetics. 21 (3), 327–340.