Conformance checking is a class of process mining techniques, which contrasts the modeled behaviors with the observed behaviors of a process, to detect, locate and explain the deviations between them. Even though deviations can occur anytime and in any perspectives, currently there is no such conformance checking technique available, which is able to take into account other perspectives than the control-flow perspective of the investigated process when computing the conformance statistics on running, incomplete cases. In this paper, a multi-perspective online conformance checking technique is introduced, which aims to confront the modeled behaviors in form of a Data Petri net process model with a stream of events as the observed behaviors. For the conformance checking, two existing techniques were merged: a prefix-alignment-based technique, which is able to compute conformance statistics for incomplete process executions by applying incremental heuristic search, and an alignment-based multi-perspective conformance checking technique, which is able to compute conformance statistics for complete process instances while focusing on multiple perspectives.