Delhi's post-monsoon and winter haze reduces visibility, causes health hazards, and interrupts usual routines. Multiple source apportionment (SA) studies recently apportioned sources and discussed organic and elemental PM source characteristics independently. To design effective pollution control strategies, it's important to obtain a comprehensive picture of particulate matter (PM_2.5) sources by doing SA on consolidated data that combines organics, inorganics, black carbon (BC), and metals. In this study, we tried to improve the understanding of PM_2.5 sources by performing double-PMF (D-PMF) analysis on a consolidated dataset encompassing non-refractory PM_2.5 factors, elements, and BC. Real-time instrumentation (HR-ToF-AMS, Xact, and Aethalometer) were used at two urban sites (IITD and IITMD) in Delhi during post-monsoon and winter seasons. The hourly average C-PM_2.5 (Composition based PM_2.5 is sum of NR-PM_2.5, BC and metals) at IITD for the overall study period (1^st Oct 2019 to 8^th Jan 2020) was 91.9 ± 56.5 μg m^-3, while at IITMD for the overall sampling period (31^st Oct 2019 to 31^st Dec 2019) was 105.2 ± 61.2 μg m⁻³. The sources identified by the double-PMF at both sites were road dust, traffic, secondary nitrate, secondary sulfate, oxidized organic aerosol (OOA), biomass burning (BB), and industrial. In contrast, fireworks were only resolved at IITD, and secondary chloride at IITMD. At IITD, the temporal variation of sources was noted between the post-monsoon, Diwali, and winter seasons. The secondary nitrate (17%, 15.8 ± 9.4 μg m^-3) and BB (39.4%, 36.6 ± 43.6 μg m^-3) were dominant during winter suggest the rapid-nighttime oxidation with favourable low temperature condition and increased heating activities, while OOA (33.4%, 17.2 ± 8.0 μg m⁻³) and secondary sulfate (12.7%, 6.5 ± 4.4 μg m^-3) were dominating during the post-monsoon at IITD due to the high photochemical oxidation and long-range transport. The fireworks (22.2%, 26.6 ± 43.8 μg m^-3) contributed a major fraction of sources during Diwali at IITD. For the concurrent measurement period (14^th Nov 2019 to 31^st Dec 2019) at both the sites, the mean hourly average concentration (C-PM_2.5) was 102.2 ± 53.2 μg m⁻³ at IITD and 99.7 ± 59.6 μg m^-3 at the IITMD site. Secondary nitrate and secondary sulfate were prevalent at IITMD, while OOA and traffic dominated at IITD. D-PMF improved interpretation of sources such as the SO₄_OA and NO₃_OA contributions to industrial sources (Pb-rich and Zn-rich) indicate the possibility of sulfate and nitrate accumulation on metal-rich particles (for example, the formation of ZnSO₄ and PbSO₄). The signals of NO₃_OA in the fireworks factor are due to the gunpowder (KNO₃), while HOA and BBOA suggest the role of burn-related organics. The elemental ratios K/Pb (17 at IITD) and K/As (137 at IITMD) in the secondary sulfate source from D-PMF further highlighted the role of coal combustion. The D-PMF results were in excellent agreement with single PMF on combined data (SC-PMF) done as a part of an extended study.