Date: 201903
Local time of day: 0601-1200
Location: ZKC.ARTCC, KS
Flight conditions: IMC
Aircraft: MD-80 Series (DC-9-80) Undifferentiated or Other Model
Operator: Air Carrier
Operating under: Part 121
Flight plan: IFR
Mission: Passenger
Flight phase: Cruise
Airspace: Class A ZKC
ATC / advisory: Center ZKC
Aircraft component: Airspeed Indicator
Component problem: Malfunctioning
Reporter organization: Air Carrier
Reporter function: Captain; Pilot Flying
Reporter qualification: Flight Crew Multiengine; Flight Crew Air Transport Pilot (ATP); Flight Crew Instrument
Human factors: Human-Machine Interface; Communication Breakdown
Second reporter function: Pilot Not Flying; First Officer
Anomaly: Aircraft Equipment Problem Critical; Deviation - Altitude Excursion From Assigned Altitude; Deviation - Speed All Types; Deviation / Discrepancy - Procedural Clearance; Inflight Event / Encounter Weather / Turbulence
Detector: Person Flight Crew
When detected: In-flight
Result: Aircraft Equipment Problem Dissipated; Flight Crew Took Evasive Action
Contributing factors: Weather; Aircraft
Primary problem: Weather

Narrative: We were at FL310 deviating around weather. Our first indications of systems failures were the Captain noticed the FMA transition to heading hold followed by the FO (First Officer) noticed F/S failure on the PFD and a Mach speed failure. Shortly thereafter A/P and A/T disengage. The Captain assumes aircraft control; he was previously also the PF (Pilot Flying). FO begins running the Mach speed failure checklist since it is the most obvious indication of failure. Shortly thereafter we notice a large split in indicated air speeds. We now suspect unreliable airspeed. The initial evaluation of the Captain's indications supported known pitch and power settings. Additionally at this point we are IMC with multiple cells in our vicinity. The Captain has already seated the flight attendants for the turbulent ride. We [advised ATC]. Shortly thereafter; while in level flight; we get an approach to stall indication; wing buffet; PF pushes over and pushes up the throttles to be followed shortly by over speed indications; assessed to be due to the barometric effects but unknown if we actually over-sped the aircraft. The threat of the weather is overridden by the need for warmer air; since we suspect pitot tube icing; so PM (Pilot Monitoring) continues the descent and deploys the speed brakes. PM transitions to FO''s instruments and cross checks the standby A/S. The maneuvering was fairly benign with minimal disturbance to the cabin. Approaching 15000 ft. the instrumentation corrects and we begin evaluating divert options. We initially ask for a vector to the closest VMC. All of the suitable airfields in the vicinity had poor ceilings and visibility. We evaluated our fuel and elected to continue to ZZZ for the weather conditions. We landed uneventfully! A factor of note is we could not communicate with ATC for a large portion of this [event] due to significant static on the radios. Engine and wing anti-ice were on and pitot heat was checked.


Second narrative: [Report narrative contained no additional information.]


Synopsis: MD80 flight crew reported airspeed indication anomaly in IMC that resulted in an altitude excursion.