EMB505 First Officer reported unknowingly entering a storm area of moderate turbulence; due to miscommunication from dispatch and planning; resulted in altitude deviation due to loss of control.

Narrative

I was departing ZZZZ1 to ferry to ZZZ1; when I saw I had missed a call from the company. I requested to stop taxiing and returned the call. The company asked if we; would be willing to go to ZZZZ to pick up passengers and take them to ZZZ as a recovery. My First Officer; was willing; as was I. Upon arriving in ZZZZ; we spoke with Dispatch and asked if they could brief me on the potential weather; as we had been informed there was a delay in our release because of routing around a little bit of weather". **I had started IOE the previous week and was not keeping up with the weather in the area. I was aware a tropical system was in the ocean; but was not aware that it had entered the area we were flying over. Nor did I have the SkyPath app open to give me more of an indication.**Our original routing had us departing ZZZZ crossing one country and crossing over another to enter the next from the south. However; shortly after getting out over the water; we were informed that the airway we were routed on was closed. The new routing took us further north. At the time we were in VMC and smooth air. After dark; we saw some weather to the south of our position and since the NEXRAD (Next Generation Weather Radar) does not have coverage in our location so we turned on our radar. We scanned up; down; in; out and were monitoring the conditions as best we could. Approximately 2 hours into the flight we encountered IMC and some light turbulence at FL400. We requested a climb to FL430. It appeared to clear up again; as if we were on top of the cloud deck and smoothed out. A few minutes later; we were back in IMC and being pelted with intense precipitation and moderate turbulence. The turbulence increased and the aircraft started to climb reaching an altitude of 43;400. I knew there was clear weather further north as I had seen on the limited NEXRAD the coastal regions were clear. I started a left turn and the aircraft started descending at 1500 fpm. I reduced thrust to keep from over speeding. The aircraft slowly came back to altitude and we ultimately exited the storm. I accept my responsibility as I am the pilot in command (PIC). I should have taken more time; and inquired more about the conditions that we were being routed around. However; the Dispatcher could have been more blunt and more specific; though I understand 'how does a pilot not know about a large storm'…"