A new self-consistent model is developed to treat the static contact of a microparticle with a flat barrier in the presence of molecular adhesion and surface roughness. Separation between their mean datum planes is modeled considering the elastic deformation of the microparticle and surface. The contact pressure is computed from the Lennard-Jones law following the Derjaguin approximation. The elastic deflection of the mean datum plane is calculated from the effective pressure by the half-space elastic theory. Roughness is modeled by introducing a Gaussian distribution to the gap between the surfaces. An effective pressure is defined as the statistical average of the contact pressure over the roughness heights. A solution satisfying all of the above conditions gives a self-consistent method of modeling adhesion between the microparticle and the flat barrier. Using collocation methods the equations are discretized as a large system of nonlinear algebraic equations. A continuation method is used to find the multiple numerical solutions for the mean separation and the effective contact pressure. Finally, adhesive contacts of both smooth and rough surfaces are simulated in a comparative manner to elucidate the features of surface roughness in the presence of molecular adhesion. The standard deviation of the Gaussian distribution is used as a parameter to assess the effects of roughness on the pull-off force. It is shown that increasing surface roughness significantly reduces the pull-off force and decreases the tendency for the microsphere to snap-on and snap-off.