Can physical and chemical changes happen together?

Yes, the physical and chemical changes can occur together.
An example is the burning of a candle. When the candle burns, the wax melts and the wick burns. Even though the wax melts, it still stays wax and there is no change in its chemical formula. Hence this is a physical change. When the wick burns, carbon dioxide is generated. This is a chemical change as a different substance than the starting substance is generated.
Similarly, eating the food involves both physical changes and chemical changes. Breaking down larger pieces of food (say bread) into smaller pieces through chewing is a physical change. Breakdown of food molecules into simpler molecules, by the action of enzymes, is a chemical change.
Another example is eating chocolate, which involves breaking it down into smaller portions (physical change) and then metabolizing it (chemical change). The burning of wood is another similar example.

Hope this helps.