In this paper, we present a new technique for simultaneous multifield optimization of the biological effect (i.e. relative biological effectiveness times dose) for intensity modulated radiotherapy with ion beams. It offers complete inverse treatment planning by taking into account planning constraints for the target volume as well as for organs at risk. The approach is based on the mixed irradiation formalism of the linear-quadratic model from radiobiology. We employ a novel objective function to directly optimize the biological effect rather than the physical dose. The required biological input data are reduced to a minimum and are completely independent from the optimization itself. They can be derived from any radiobiological model or even from directly measured data. The new optimization method was fully integrated into our inverse treatment planning tool KonRad. Comparisons with the TRiP98 treatment planning code were done for simple spread-out Bragg peaks as well as for three-dimensional treatment plans, where all fields were optimized separately. While the agreement between both planning systems was very good, the calculation time was substantially reduced in KonRad. By enabling the multifield optimization, the quality of the treatment plans and the sparing of healthy tissues can be clearly improved.