No its not how it should be, but can have a lot of different reasons.
Check for external leak, water pump, hoses, radiator, heater core etc. If everything is in order I would lift oil filler cap and oil stick check so oil isnt contaminated with water (grey sludge). If oil also looks good you have an internal leak either head gasket or cylinder foot gaskets.
So after eliminating external leaks and car dont smoke white while driving (water enters combustion chamber) and oil looks good I would keep filling bottle and check oil filler cap/ dipstick every fuel fill.