This paper presents a novel type of stochastic resonance (SR) with a mixture of sub- and supra-threshold stimuli in a population of neuron models beyond regular SR and Supra-threshold SR (SSR) phenomena. We investigate through computer simulations if the novel type of SR can be observed or not, using the mutual information (MI) estimated from a population of neural spike trains as an index of information transmission. Computer simulations showed that the MI had a typical type of SR curves, even when the balance between sub-and supra-threshold stimuli was varied, suggesting the novel type of SR. Moreover, the peak of MI increased as the balance of supra-threshold stimuli got stronger, i.e., as the situation was getting close to the SSR from the regular SR. This finding could accelerate our understanding about how fluctuations play a role in processing information carried by a mixture of sub-and supra-threshold stimuli.