Robin,
You can not log time as Pilot in command because that would make the other person a passenger and you can't do that because you don't have the required take-off and landings.
You can't log the time as dual unless the other pilot (pilot in command) is an instructor.
You can log the flight departure, and arrival times and in the appropriate column record the number of take-off and landings you completed as sole manipulator of the controls.
----------
Bose,
Try JAR-FCL or LASORS.
The requirement for carrying passengers is that the pilot in command must have completed 3 take-offs and landings as sole manipulator of the controls in the last 90 days.
Sole manipulator of the controls means just that nothing more and nothing less.
There is noting about dual, in command, or solo. That is because the capacity of the pilot makes no difference it is the performance of the take-off and landings as "sole manipulator of the controls" that counts.
That is why you now need to log the number of take-off and landings you complete on each flight so that you can easily check that you have enough.
If you want to pay an instructor to sit beside you while you do the required take-offs and landings as sole manipulator of the controls then good. But the fact that there is an instructor along makes absolutely no difference in how the requirement is met.
Regards,
DFC