A joint transmitter-receiver energy harvesting model is considered, where both the transmitter and receiver are powered by (renewable) energy harvesting source. Given a fixed number of bits, the problem is to find the optimal transmission power profile at the transmitter and ON-OFF profile at the receiver to minimize the transmission time. With infinite capacity at both the transmitter and receiver, optimal offline and optimal online policies are derived. The optimal online policy is shown to be two-competitive in the arbitrary input case. With finite battery capacities at both ends, only random energy arrival sequence with given distribution are considered, for which an online policy with bounded expected competitive ratio is proposed.