Fast neutron, gamma-ray, and boron doses have different relative biological effectiveness (RBE). In boron neutron capture therapy (BNCT), the clinical dose is the total of these dose components multiplied by their RBE. Clinical dose monitoring is necessary for quality assurance of the irradiation profile; therefore, the fast neutron, gamma-ray, and boron doses should be separately monitored. To estimate these doses separately, and to monitor the boron dose without monitoring the thermal neutron fluence, the authors propose a triple ionization chamber method using graphite-walled carbon dioxide gas (C-CO2), tissue-equivalent plastic-walled tissue-equivalent gas (TE-TE), and boron-loaded tissue-equivalent plastic-walled tissue-equivalent gas [TE(B)-TE] chambers. To use this method for dose monitoring for a neutron and gamma-ray field moderated by D2O from a Be-covered Li target (Be-covered Li BNCT field), the relative sensitivities of these ionization chambers are required. The relative sensitivities of the TE-TE, C-CO2, and TE(B)-TE chambers to fast neutron, gamma-ray, and boron doses are calculated with the particle and heavy-ion transport code system (PHITS). The relative sensitivity of the TE(B)-TE chamber is calculated with the same method as for the TE-TE and C-CO2 chambers in the paired chamber method. In the Be-covered Li BNCT field, the relative sensitivities of the ionization chambers to fast neutron, gamma-ray, and boron doses are calculated from the kerma ratios, mass attenuation coefficient tissue-to-wall ratios, and W-values. The Be-covered Li BNCT field consists of neutrons and gamma-rays which are emitted from a Be-covered Li target, and this resultant field is simulated by using PHITS with the cross section library of ENDF-VII. The kerma ratios and mass attenuation coefficient tissue-to-wall ratios are determined from the energy spectra of neutrons and gamma-rays in the Be-covered Li BNCT field. The W-value is calculated from recoil charged particle spectra by the collision of neutrons and gamma-rays with the wall and gas materials of the ionization chambers in the gas cavities of TE-TE, C-CO2, and TE(B)-TE chambers (10B concentrations of 10, 50, and 100 ppm in the TE-wall). The calculated relative sensitivity of the C-CO2 chamber to the fast neutron dose in the Be-covered Li BNCT field is 0.029, and those of the TE-TE and TE(B)-TE chambers are both equal to 0.965. The relative sensitivities of the C-CO2, TE-TE, and TE(B)-TE chambers to the gamma-ray dose in the Be-covered Li BNCT field are all 1 within the 1% calculation uncertainty. The relative sensitivities of TE(B)-TE to boron dose with concentrations of 10, 50, and 100 ppm 10B are calculated to be 0.865 times the ratio of the in-tumor to in-chamber wall boron concentration. The fast neutron, gamma-ray, and boron doses of a tumor in-air can be separately monitored by the triple ionization chamber method in the Be-covered Li BNCT field. The results show that these doses can be easily converted to the clinical dose with the depth correction factor in the body and the RBE.