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135.293(a)(7)(iii) requires that pilots be tested on:
(iii) Operating in or near thunderstorms (including best penetrating altitudes), turbulent air (including clear air turbulence), icing, hail, and other potentially hazardous meteorological conditions;
So what are the best penetrating altitudes when forced to operate in a thunderstorm?
The most obvious answer is to stay out of it in the first place, but the reg requires us to come up with an answer....
The obvious answer you mentioned should be reiterated: Avoid thunderstorms whenever possible! Just because there are "best penetrating altitudes" doesn't change the fact that thunderstorms are extremely hazardous to aircraft and should be avoided in the first place.
With that said, the FAA's Advisory Circular 00-24C mentions that, if unable to avoid penetrating a thunderstorm:
To avoid the most critical icing, establish a penetration altitude below the freezing level or above the level of -15ºC.
This is to help minimize rapid accumulation of clear ice:
Supercooled water freezes on impact with an aircraft. Clear icing can occur at any altitude above the freezing level but at high levels, icing from smaller droplets may be rime or mixed rime and clear. The abundance of large, supercooled water droplets makes clear icing very rapid between 0ºC and -15ºC, and encounters can be frequent in a cluster of cells. Thunderstorm icing can be extremely hazardous.
Another point to mention is that, regardless of there being a recommended "penetration altitude," it is important to maintain a constant attitude, not altitude:
It is almost impossible to hold a constant altitude in a thunderstorm, and maneuvering in an attempt to do so greatly increases stress on the aircraft. Stresses are least if the aircraft is held in a constant attitude.
But again, emphasizing the dangers of thunderstorms, the circular states:
Never regard any thunderstorm lightly, even when radar observers report the echoes are of light intensity. Avoiding thunderstorms is the best policy.
and
Weather recognizable as a thunderstorm should be considered hazardous, as penetration of any thunderstorm can lead to an aircraft accident and fatalities to those on board.
0 AGL. Do not ever penetrate a thunderstorm in an airplane. It is stupid. People die that way every year.
I was asked this question on a 135 ride. Stumped for an answer, I was told I will get comfortable flying through if I wanted the job. As this was in the plains, 5000 or 6000 depending on the direction of the flight was the recipe. Not high enough for icing most of the time, yet enough altitude to recover from downdrafts. This also kept us in Approach/Departure airspace and their radar was much better at depicting live weather, as opposed to what the Center controllers handling higher altitudes would be seeing. Asking for vectors through level 1 or 2 was OK but taking level 3 when unavoidable was a rough ride. Using tango prefix in the call sign let them know I was neither a doctor nor an attorney. Night time lowered their workload so they could find a way to get us across squall lines, coming up with diversions around this stuff. After getting my head slammed into the ceiling I learned to hunch when it got bumpy. Few months of that, seeing thundersnow and learning that lightning flashes looks pink when you get close made me go back to flying passengers. Soon after the Check 21 legislation killed that whole business model but for many many years before me guys and gals were doing this every night with no accidents or incidents related to the practice.
