Criteria crit = session.createCriteria(CalendarEventTO.class);
crit.add(Expression.between("start", firstOfMonth, lastOfMonth));
crit.list();

import net.sf.hibernate.expression.AbstractCriterion;
import net.sf.hibernate.engine.SessionFactoryImplementor;
import net.sf.hibernate.engine.TypedValue;
import net.sf.hibernate.HibernateException;
import net.sf.hibernate.type.IntegerType;
import net.sf.hibernate.util.StringHelper;

import java.util.Map;

public class DateMonthEqExpression extends AbstractCriterion {

   private final String  propertyName;
    private final Integer month;

   DateMonthEqExpression(String propertyName, Integer month) {
      this.propertyName = propertyName;
        this.month = month;
   }

   public String toSqlString(SessionFactoryImplementor sessionFactory, Class persistentClass, String alias, Map aliasClasses) throws HibernateException {
        String sql = StringHelper.join(
         " and ",
         StringHelper.prefix(
                StringHelper.suffix( getColumns(sessionFactory, persistentClass, propertyName, alias, aliasClasses), ")} = ?" ),
                "{fn MONTH(")
      );

        return sql;
   }

   public TypedValue[] getTypedValues(SessionFactoryImplementor sessionFactory, Class persistentClass, Map aliasClasses) throws HibernateException {
        TypedValue tv = new TypedValue(new IntegerType(), month);
        return new TypedValue[] {tv};
    }

   public String toString() {
      return propertyName + " equals " + month;
   }

}

crit.add(DateExpression.dateMonthEq("start", 3));