Associated production of bottomonia and open charm hadrons in $pp$ collisions at $sqrt{s}=7$ and $8$TeV is observed using data corresponding to an integrated luminosity of 3$fb^{-1}$ accumulated with the LHCb detector. The observation of five combinations, $Upsilon(1S)D^0$, $Upsilon(2S)D^0$, $Upsilon(1S)D^+$, $Upsilon(2S)D^+$ and $Upsilon(1S)D^+_{s}$, is reported. Production cross-sections are measured for $Upsilon(1S)D^0$ and $Upsilon(1S)D^+$ pairs in the forward region. The measured cross-sections and the differential distributions indicate the dominance of double parton scattering as the main production mechanism. This allows a precise measurement of the effective cross-section for double parton scattering.