The problem here is the use of terminology which means different things to different people. To me - following the Austrian school - inflation and deflation are monetary phenomena. If the money supply is increasing, we have inflation and if it decreasing then we have deflation. By this definition it is not possible to have both at once.

What you are describing is the movement of prices, which often follow changes in the money supply, but not always if other factors are at play. If the money supply were suddenly doubled while all else stayed the same, you would expect prices to double eventually as well, but all else does not necessarily stay the same.

For instance, increases in the M3 of some 13% per year in recent years have not ignited a wage/price spiral due to global competition keeping a lid on both wages and the prices of manufactured goods. Wages have stagnated, while cheap plastic tat from China has fallen in price. Stagnating wages set against a backdrop of rising monetary inflation means that wages are falling in real terms. Falling prices for manufactured goods against the same backdrop mean that prices have been crashing in real terms.

Similarly, prices can rise against a backdrop a falling money supply, which means they would be going through the roof in real terms. This could well happen to oil and food after an initial price collapse, as there are many circumnstances that could hit supply as hard as deflation will hit demand. You could indeed see food and energy prices rise while asset prices continue to fall, but calling it inflation and deflation confuses the issue.