I appreciate that there's an impact from the quality of the lines, and that EMI from the adjacent power is likely an issue, though the EMI is mitigated through the use of twisted cable pairs and wire transposition.
The fact that you could get signal at all means the interference is likely much less an issue that your distance to their POP and the equipment they are using.
The orthogonal frequency-division multiplexing used in modern DSL standards were specifically developed to deal with poor quality conductors, frequency skew, EMI, etc. They work by multiplexing many many "slow" streams (at differing frequencies) which in aggregate provide you a fast connection. If you can get 1.5Mbit, that means the lines are "good enough" and extra speed is more or less a matter of the symbol rate and the number of channels that can be bonded.
I am fairly confident that if they were promising you between 1 and 3Mbit, and you are getting 1.5Mbit that they are using ADSL. Should they upgrade their equipment to VDSL2 you should be able to get between 25 and 50Mbit with the same quality lines.