I am not looking for RT-AWD cars with automatic AWD which are usually FWD but permanent AWD cars.
You can get the CR-V, Pilot, Ridgeline, and Crosstour with the AWD option. Understand that these vehicles will not engage all four wheels at all times. If you are looking for a vehicle where all four wheels are engaged all of the time, I don't think you'll find one, whether it's a Honda or not. 4WD/AWD vehicles are designed with a bias built into the transfer case which puts ~60% of the power to the main drive wheels and the rest to the alternate wheels. The alternate wheels do not engage until the mains start to slip. This is called a torsion bias.
Cars equipped with Variable Torque Management 4WD (VTM-4) fall somewhere in between. While normally FWD, they engage rear wheels on any acceleration and allow driver to lock all-wheel drive on low speeds and gears. VTM-4 has been used on Honda Pilot and Honda Ridgeline.