It is known that potential difference on metal/electrolyte or any kind of interphase can't be measured since voltmeter needed to measure it is made of metal which would in contact with metal and solution develop its own potential difference at interphase and as such affect the measurement. To solve this problem, potential is measured with respect to SHE. What I don't understand is that if you want to measure the electrode potential with respect to SHE, voltmeter needs to come in contact with two metal electrodes (one is electrode which potential you want to measure and the other is SHE) which will again create potential difference between the electrodes and voltmeter since two different metals in contact create potential difference between them. Can you explain?
It is the same as measurement of voltage difference at any electronic circuit. The fact the metallic measuring points are attached to electrochemical electrodes is not relevant here.
Yes, there is metal contact potential difference, but it very low and very probably mutually canceling.
It is measured with the help of a reference electrode known as the standard hydrogen electrode (abbreviated to SHE). The electrode potential of SHE is 0 Volts. The standard electrode potential of an electrode can be measured by pairing it with the SHE and measuring the cell potential of the resulting galvanic cell.