Consider setting index on each data frame and then run the horizontal merge with pd.concat
:
dfs = [df.set_index(['profile', 'depth']) for df in [df1, df2, df3]]
print(pd.concat(dfs, axis=1).reset_index())
# profile depth VAR1 VAR2 VAR3
# 0 profile_1 0.5 38.198002 NaN NaN
# 1 profile_1 0.6 38.198002 0.20440 NaN
# 2 profile_1 1.1 NaN 0.20442 NaN
# 3 profile_1 1.2 NaN 0.20446 15.188
# 4 profile_1 1.3 38.200001 NaN 15.182
# 5 profile_1 1.4 NaN NaN 15.182