We present near-infrared and optical photometry, plus optical spectroscopy of two stripped-envelope supernovae (SNe) 2010O and 2010P that exploded in two different components of an interacting luminous infrared galaxy Arp 299 within only a few days of one another. SN 2010O is found to be photometrically and spectroscopically similar to many normal Type Ib SNe and our multiwavelength observations of SN 2010P suggest it to be a Type IIb SN. No signs of clear hydrogen features or interaction with the circumstellar medium are evident in the optical spectrum of SN 2010P. We derive estimates for the host galaxy line-of-sight extinctions for both SNe, based on both light curve and spectroscopic comparison finding consistent results. These methods are also found to provide much more robust estimates of the SN host galaxy reddening than the commonly used empirical relations between extinction and equivalent width of Na i D absorption features. The SN observations also suggest that different extinction laws are present in different components of Arp 299. For completeness, we study high-resolution pre-explosion images of Arp 299 and find both SNe to be close to, but not coincident with, extended sources that are likely massive clusters. A very simple model applied to the bolometric light curve of SN 2010O implies a rough estimate for the explosion parameters of E-k approximate to 3 x 10(51) erg, M-ej approximate to 2.9 M-circle dot and M-Ni approximate to 0.16 M-circle dot.