This paper investigates transmission strategies for joint wireless information and energy transfer in a two-user MIMO interference channel, in which each receiver either decodes the incoming information data (information decoding, ID) or harvests the RF energy (energy harvesting, EH) to operate with a potentially perpetual energy supply. In the two-user interference channel, we have four different scenarios according to the receiver mode - (ID1, ID2), (EH1, EH2), (EH1, ID 2), and (ID1, EH2). For single-operation modes such as (ID1, ID2) and (EH1, EH2), the optimal transmission strategies achieving either maximum information bit rate or maximum harvested energy are derived - iterative water filling and rank-one energy beamforming. For (EH1, ID2), and (ID 1, EH2), the achievable rate-energy (R-E) tradeoff region is investigated when one of the transmitters takes a rank-one energy beamforming and the other transmitter takes 'water-filling-like' approach. Here, for the rank-one energy beamforming, the transmitter can take two different strategies - maximum energy beamforming (MEB) and minimum leakage beamforming (MLB). Finally, a new rank-one energy beamforming strategy - signal-to-leakage-and- energy ratio (SLER) maximization beamforming - is proposed.