The complex flowfield in a gas turbine combustor makes cooling the liner walls a challenge. In particular, this paper is primarily focused on the region surrounding the dilution holes, which is especially challenging to cool due to the interaction between the effusion cooling jets and high-momentum dilution jets. This study presents overall effectiveness measurements for three different cooling hole patterns of a double-walled combustor liner. Only effusion hole patterns near the dilution holes were varied, which included: no effusion cooling; effusion holes pointed radially outward from the dilution hole; and effusion holes pointed radially inward toward the dilution hole. The double-walled liner contained both impingement and effusion plates as well as a row of dilution jets. Infrared thermography was used to measure the surface temperature of the combustor liners at multiple dilution jet momentum flux ratios and approaching freestream turbulence intensities of 0.5% and 13%. Results showed the outward and inward geometries were able to more effectively cool the region surrounding the dilution hole compared to the closed case. A significant amount of the cooling enhancement in the outward and inward cases came from in-hole convection. Downstream of the dilution hole, the interactions between the inward effusion holes and the dilution jet led to lower levels of effectiveness compared to the other two geometries. High freestream turbulence caused a small decrease in overall effectiveness over the entire liner and was most impactful in the first three rows of effusion holes.