Gbarrios,I was checking the website and I noticed that the Intel® Core™ i3-3250 Processor is not on the data base. So that could be the reason why it does not appear on the compatibility list with all these motherboards.
If I check on ark.intel.com, it shows all compatible chipsets and the H61 and H77 express chipset are included on the list. http://ark.intel.com/products/74744/Intel-Core-i3-3250-Processor-3M-Cache-3_50-GHz?q=3250
I will forward this information to the corresponding department so they can add this processor to the list.
Regarding the compatibility between the Dh61BE or the DH61HO and a 3rd Generation processor, the following link will provide you additional information on this question. http://www.intel.com/support/motherboards/desktop/sb/CS-033076.htm
For example, in order to use the i3-3250 on a DH61BE motherboard, you would need a 2nd generation processor in order to update the BIOS to the transition version, in this case was 0035. Then, install BIOS version 0041.
Once these 2 versions are installed on the board, you should be able to use the processor.