Dielectric barrier discharges (DBD) in air at atmospheric pressure and at low frequency are mainly constituted of thin transient plasma filaments (or microdischarges) with radii of a few hundreds of micrometers. In this work, we consider a point-to-plane geometry with the dielectric covering the plane electrode. Plasma filaments are initiated by streamers, starting from the high-field region close to the point electrode. The plasma filaments deposit charges on the dielectric plate which screen the electric field and lead to an extinction of the discharge filaments. In this work we experimentally demonstrate the synchronous start of several filaments in a time range of less than a few tens of nanoseconds and we show that the charges deposited on the dielectric have a strong impact on the discharge structure. This is validated using a simple electrostatic model. Then, the dynamics of the 2D streamer propagation in the gas gap and its interaction with the dielectric plane is calculated. The influence of space charges and surface charges on the discharge structure are discussed and compared with the experiment.