AFAIS, Bluray discs are all region independent. I own a PS3 that plays EVERY bluray you throw at it, save for the Chinese regions.
That is not correct. PS3s are very much region dependent and in fact there is no hack till date to break the region coding on PS3s. You may be confusing blu-ray disks with PS3 games, which are not region coded and thus play on PS3s from all regions.
I have the CECHH version.
Actually the 'CECHH' you mention is an incomplete model number. This portion of the model number only tells you that your PS3 is a 40GB PS3 with the 65nm Cell & 65nm RSX processor. The alphabets are followed by 2 digit numbers. It is these two digits that identify the Region/Country of the PS3 and thus which region blu-ray discs the PS3 is compatible with.
The following list can be used to determine which Region the PS3 is compatible with:
'xx' these two digits identify the Region/Country
'00' represents 'Japan' which is 'Blu-ray - Region A' & 'DVD - Region 2 'NTSC')
'01' represents 'North America' which is 'Blu-ray - Region A' & 'DVD - Region 1 'NTSC')
'02' represents 'Australia/New Zealand' which are 'Blu-ray - Region B' & 'DVD - Region 4 'NTSC/PAL')
'03' represents 'U.K./Ireland' which are 'Blu-ray - Region B' & 'DVD - Region 2 'NTSC/PAL')
'04' represents 'Europe/Middle East/Africa' which are 'Blu-ray - Region B' & 'DVD - Region 2 'NTSC/PAL')
'06' represents 'Singapore' which is 'Blu-ray - Region A' & 'DVD - Region 3 'NTSC')
'08' represents 'India/Russia' which are 'Blu-ray - Region C' & 'DVD - Region 5 'NTSC/PAL')
I intend to buy discs from USA. I think they should work.
If you intend to buy Blu-ray discs (Region A encoded) from the US, then make sure your PS3 model number ends with either '00', '01' or '06'. If you intend to buy DVDs (Region 1 encoded) from the US, then make sure your PS3 model number ends with '01'.
Blu-rays that are A/B/C encoded and DVDs that are Region free will of course play on all PS3s.