Measuring the photon number distribution (PND) of optical states allows one to extract metrics of non-classicality of fundamental and technological relevance, but requires in principle the use of detectors with photon number resolving capabilities (PNR). Here we reconstruct the PND of two-mode pulsed squeezed light generated from a silicon nitride microresonator using threshold detectors and variable optical attenuations. The PNDs are characterized up to $\sim 1.2$ photons/pulse, corresponding to an on-chip squeezing level of $6.2(2) \ \mathrm{dB}$ and a noise reduction factor (photon number difference squeezing) of $3.8(2) \ \mathrm{dB}$. The analysis performed on the photon-number basis allows us to additionally characterize the influence of a spurious thermal background field that reduces the photon number correlations.