  The ensemble of $L \times L$ power-law random banded matrices, where the
random hopping $H_{i,j}$ decays as a power-law $(b/| i-j |)^a$, is known to
present an Anderson localization transition at $a=1$, where one-particle
eigenfunctions are multifractal. Here we study numerically, at this critical
point, the statistical properties of the transmission $T_2$ for two
distinguishable particles, two bosons or two fermions. We find that the
statistics of $T_2$ is multifractal, i.e. the probability to have $T_2(L) \sim
1/L^{\kappa}$ behaves as $L^{\Phi_2(\kappa)}$, where the multifractal spectrum
$\Phi_2(\kappa)$ for fermions is different from the common multifractal
spectrum concerning distinguishable particles and bosons. However in the three
cases, the typical transmission $T_2^{typ}(L)$ is governed by the same exponent
$\kappa_2^{typ}$, which is much smaller than the naive expectation
$2\kappa_1^{typ}$, where $\kappa_1^{typ}$ is the typical exponent of the
one-particle transmission $T_1(L)$.
