Another example of a change that is both chemical and physical is the burning of wood. The moisture present in the wood turns to vapor, when heated, which is a physical change. The actual burning of wood will generate carbon dioxide (among other products) and is a chemical change.
Another example is eating chocolate, which is both a physical change (breaking of chocolate into smaller pieces or melting of chocolate) and a chemical change (breaking of chocolate molecules into simpler molecules, etc.).
A third example is weathering in nature. Rocks are physically changed by wind, running water, expansion of ice as it freezes, abrasive wind and water-borne sediments. They are chemically changed by oxygen, acid rain and acidic compounds produced by decomposers.
The cycle of an internal combustion engine involves both a physical and chemical change. Gasoline is vaporized and the air in the cylinders is compressed, a physical change, before being ignited and combusting, a chemical change.